5. Find the second solution by reduction of order method: (1- 2x? y" + 4xy' – 4y=0 y, (x)=-2x

Q: Present your work in a clean and formal way!.. 1. Solve the initial value problem and determine the…

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Q: 1) Use reduction of order method with y₁ (x) = e-2x to find a second solution y2 for the DE: y" - 4y…

A: Solution :-

Q: 2. xyy' = 1+ y? ; when x = 2, y = 3

A: Given xyy' = 1+y2 and  x=2 >>> y=3

Q: First note that yı(x) = x is one solution of Legendre's equation of order 1, (1 – x²)y" – 2xy' + 2y…

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Q: Given that y' = 2x + x²y, where y(0) = -1 with step size h=0.1. Estimate the values of y(0.2) using…

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Q: A 2nd order homogenous LDE has a solution xe-3x Find its general solution.

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Q: Solve y"-(y-y, using fourth order Runge-Kutta method for a02 correct to four decimal places with the…

A: To solve the second order ordinary differential equation by fourth order Runge-Kutta method, convert…

Q: 1) Approximate the value of y for 0sxs1.5 using the Euler method if the step length is h=0.5.

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Q: Find the general solution using reduction of order.

A: As per our guidelines we are supposed to answer only one question. Kindly repost others question as…

Q: Solve the diffevential cauationm. du e cosn=0,0 X2015,40)-a. Alam - Moislton method with h=0.4.

A: The given differential equation is, dydx+y-e-xcosx=0

Q: Suppose we are given y₁) and y2(x) (with y₁ ‡ y2), which are two different solutions of a…

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Q: Use Euler method to approximate the value of y(0.1), given               y' - x2 - y = 5 ,  y(0) =…

A: Euler Method:-  For a function fx, y the method is xi+1=xi+∆xyi+1=yi +h fxi, yi; i=0, 1, 2,... Here,…

Q: 5. Apply the Euler-Cauchy method with step length h to the problem y'=-y, y(0)=1 h = 0.1

A: y' = -y , y(0)=1 and h=0.1 f(x,y) = y' = -y  x0 = 0   and  y0 = 1

Q: Solve x' = –3x – 5y, y' = x - y with initial conditions x(0) = –1, y(0) = 1.

A: Introduction: In order to solve x' = Ax, we1. First, determine the eigenvalue and eigenvectors of…

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A: Given: y(t) changes according to the law, dydt=-0.05y2 where, y is the concentration in moles per…

Q: e) y-2y'+y

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Q: 5. Obtain the particular solution. y'"-2 y'+2 y=3e" cos 2x; when x 0, y=2,y'=3

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Q: Use the classical fourth order RK method to integrate (a) f(x, y) = -2x3 + 12x2 - 20x + 8.5 using a…

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Q: You can think of the first two cases as being performed in vacuum (no friction) and air of water…

A: Let's find.

Q: Choose the solution value of x'' + w2x = fsinwt with initial conditions x(0) = 0 and x'(0) = 0

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Q: 2xyy'=1+y; whent = 2, y = 3 Ans. y = 5x-1

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Q: Use the classical fourth order RK method to integrate (a) f(x, y) = -2x3 +12x2 - 20x + 8.5 using a…

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Q: Find the general solution of the Cauchy-Euler equation: X^3y’’’ - x^2y’’ + 2xy’ - 2y = x^3

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Q: Solve the separable initial value problem. 1. y' = In(x)(1+y²), y(1) = 1 → y= 2. y =…

A: Use the following formulas 1.∫xndx=xn+1n+1+c2.∫11+x2dx=tan-1x+c3,∫ln x dx=xln x-x+c

Q: The solution of y" – 2y' + y = 0 with initial conditions y(0) = 1 and y'(0) = 0 is given by?

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Q: Use the fourth-order Runge-Kutta method to solve y' = e-2x - 2y on [0, 0.4] with y(0) = 2 using step…

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Q: Solve the problem := (1+ 4x)/y over the interval from from x = 0 to x = 1 using a step size of 0.25…

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Q: 2. Show that the substitution z=y(1-n) will reduce the Bernoulli Equation y' + f(x)y = Q(x)yn to a…

A: The solution is given as

Q: 4) One of the solution of the equation y"(x) + p(x)y' (x) + q(x)y(x) = 0 is given by yı (x) =…

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Q: Employ the Classical RK-4 method to integrate the given equations from x=0 to x=1 using at least one…

A: Assume, dy/dx: f(x,y,z) dz/dx=g(x,y,z) Here, x0=0, y0=2, z0=4

Q: 2. Estimate the solution of 3x = ex + 2 with po = 1, p1 = 1.8 using SECANT METHOD. Find 2 %3D…

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Q: 8. Find the particular solution that satisfies the initial condition. y'+y = 6e*, Initial Condition:…

A: Find the particular solution

Q: 22) Use Euler method to estimate the solution of the ODE y' (xy?) ,y(1) = 2, h = 0.1 at x = 1.2

A: using the Euler's rule: yi+1=yi+hf(xi,yi) we will find the solution of given ODE we have…

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Q: 7. Obtain the particular Solution by satisfying the conditions indicated. 3x dy; when x = 2, y = -1.

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Q: Solve numerically y'=x y y(0)=1 for y(0.1)and y(0.2) by modified Euler's method.

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Q: 2. Given y' = x² + y . With y=-1 when x=0. b. Calculate y(0.4) and y(0.6) using modified Euler…

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Q: y" - 5y'=x-2, when x = 0, y = 0, y = 2

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Q: Use Euler method to approximate the value of y(0.1), given y' - 4y = 3x2, y(0) = 5 with Ax = 0.02

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Q: yp=u1x+u2x^-2 is the particular solution proposed for the nonhomogeneous Cauchy-Euler equation…

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Q: Compute the general solution valid near the origin ((+4x² )y" - By = O 'y= s{1 - 4x°) + a»\x=…

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Q: A- solve = x + y² with condition y (0) = 1, x o= 0 to x =0.2 and h = 0. by Rung kutta dx method 4th

A: The given differential equation is dydx=x+y2 with conditions y0=1, x0=0 to x=0.2 and h=0.1.

Q: 4. Use the method of undetermined coefficients to find a particular solution to the system below.…

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Q: 6. Find the particular solution of 2xydx + (y² – x²)dy = 0 ;where y = 2 and x =

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Q: Find the Bolution to the initial value problem. | -y = 2€ %3D %3D

A: Given IVPy'''-y'=2e-t+9e2t  ; y(0)=0 ,  y'(0)=-1   , y"(0)=2 to find the the general solution use…

Q: Solve (5x2y2 O a. b. 2 ln 3 In a In xy² + 17y²) dx (x+2)³(x²+9) y³ |(x+2)³(x²+9) Y - -1 3 tan-¹() =…

A: Given 5x2y2-xy2+17y2dx-x3y+2x2y+9xy+18ydy=0

Q: 7.Obtain the particular solution of (1 – xy)-2dx + [y? + x²(1 – xy)-²]dy = 0 when x = 2, y = 1

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Q: Find the particular solution of xy' - 4y = 0 ; initial condition y = 2 when x = 1.

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Unitary Method

The word “unitary” comes from the word “unit”, which means a single and complete entity. In this method, we find the value of a unit product from the given number of products, and then we solve for the other number of products. 

Speed, Time, and Distance

Imagine you and 3 of your friends are planning to go to the playground at 6 in the evening. Your house is one mile away from the playground and one of your friends named Jim must start at 5 pm to reach the playground by walk. The other two friends are 3 miles away.

Profit and Loss

The amount earned or lost on the sale of one or more items is referred to as the profit or loss on that item.

Units and Measurements

Measurements and comparisons are the foundation of science and engineering. We, therefore, need rules that tell us how things are measured and compared. For these measurements and comparisons, we perform certain experiments, and we will need the experiments to set up the devices.